On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations

✍ Scribed by V. B. Matveev; A. O. Smirnov

• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 264 KB
• Volume: 14
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00403466

✦ Synopsis

Recently, considerable progress has been made in understanding the nature of the algebrogeometrical superposition principles for the solutions of nonlinear completely integrable evolution equations, and mainly for the equations related to hyperelliptic Riemann surfaces. Here we find such a superposition formula for particular real solutions of the KP and Boussinesq equations related to the nonhyperelliptic curve e94 = (2 -El) (2 -E2) (2 -E3) (2 -E4). It is shown that the associated Riemann theta function may be decomposed into a sum containing two terms, each term being the product of three one-dimensional theta functions. The space and time variables of the KP and Boussinesq equations enter into the arguments of these one-dimensional theta functions in a linear way.